# Find 2 consecutive integers with a Product of 72

The    of consecutive integers equals

We need two consecutive integers (n) and (n + 1) who have a product = 72

## Setup relational equation:

We need to find two integers, n and n + 1 who have a product of 72
n * (n + 1) = 72
Multiplying through, we get n2 + n = 72
Rearranging the equation we get n2 + n - 72 = 0

## Now that it is in Quadratic Format, determine a, b, and c:

a = 1, b = 1, and c = -72
Solution 1 = ½(-b + √b2 - 4ac)
Solution 1 = ½(-1 + √12 - 4 * 1 * -72)
Solution 1 = ½(-1 + √1 - -288)
Solution 1 = ½(-1 + √289)
Solution 1 = ½(-1 + 17)
Solution 1 = ½(16)
Solution 1 = 8

Solution 2 = Solution 1 + 1
Solution 2 = 8 + 1
Solution 2 = 9

Also, since the product of 2 negative #'s is positive, another solution is:
Solution 3 = (-1 * 8) * (-1 * 9)
Solution 3 = -1 * 8
Solution 3 = -8
Solution 4 = -1 * 9
Solution 4 = -9

Since 8 * 9 = -8 * -9 = 72, we have our solutions.

8, 9, -8, -9

### How does the Consecutive Integer Word Problems Calculator work?

Calculates the word problem for what two consecutive integers, if summed up or multiplied together, equal a number entered.
This calculator has 1 input.

### What 2 formulas are used for the Consecutive Integer Word Problems Calculator?

1. n + (n + 1) = Sum of Consecutive Integers
2. n(n + 1) = Product of Consecutive Integers

For more math formulas, check out our Formula Dossier

### What 6 concepts are covered in the Consecutive Integer Word Problems Calculator?

consecutive integer word problems
consecutive integers
n, n + 1
integer
a whole number; a number that is not a fraction
...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...
product
The answer when two or more values are multiplied together
sum
the total amount resulting from the addition of two or more numbers, amounts, or items
word problem
Math problems involving a lengthy description and not just math symbols